Mathematics

12 pages, 675 KiB

Open AccessArticle

Interpretable Embeddings for Next Point-of-Interest Recommendation via Large Language Model Question–Answering

by Jiubing Chen, Haoyu Wang, Jianxin Shang and Chaomurilige

Mathematics 2024, 12(22), 3592; https://doi.org/10.3390/math12223592 (registering DOI) - 16 Nov 2024

Next point-of-interest (POI) recommendation provides users with location suggestions that they may be interested in, allowing them to explore their surroundings. Existing sequence-based or graph-based POI recommendation methods have matured in capturing spatiotemporal information; however, POI recommendation methods based on large language models [...] Read more.

Next point-of-interest (POI) recommendation provides users with location suggestions that they may be interested in, allowing them to explore their surroundings. Existing sequence-based or graph-based POI recommendation methods have matured in capturing spatiotemporal information; however, POI recommendation methods based on large language models (LLMs) focus more on capturing sequential transition relationships. This raises an unexplored challenge: how to leverage LLMs to better capture geographic contextual information. To address this, we propose interpretable embeddings for next point-of-interest recommendation via large language model question–answering, named QA-POI, which transforms the POI recommendation task into obtaining interpretable embeddings via LLM prompts, followed by lightweight MLP fine-tuning. We introduce question–answer embeddings, which are generated by asking LLMs yes/no questions about the user’s trajectory sequence. By asking spatiotemporal questions about the trajectory sequence, we aim to extract as much spatiotemporal information from the LLM as possible. During training, QA-POI iteratively selects the most valuable subset of potential questions from a set of questions to prompt the LLM for the next POI recommendation. It is then fine-tuned for the next POI recommendation task using a lightweight Multi-Layer Perceptron (MLP). Extensive experiments on two datasets demonstrate the effectiveness of our approach. Full article

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20 pages, 11411 KiB

Open AccessArticle

Modeling and Nonlinear Dynamic Characteristics Analysis of Fault Bearing Time-Varying Stiffness-Flexible Rotor Coupling System

by Renzhen Chen, Jingyi Lv, Jing Tian, Yanting Ai, Fengling Zhang and Yudong Yao

Mathematics 2024, 12(22), 3591; https://doi.org/10.3390/math12223591 (registering DOI) - 16 Nov 2024

Abstract

There is a complex dynamic interaction between the aero-engine bearing and the rotor, and the resulting time-varying system parameters have an impact on the nonlinear dynamic characteristics of the rolling bearing-flexible rotor system. In this study, the interaction between the time-varying stiffness of [...] Read more.

There is a complex dynamic interaction between the aero-engine bearing and the rotor, and the resulting time-varying system parameters have an impact on the nonlinear dynamic characteristics of the rolling bearing-flexible rotor system. In this study, the interaction between the time-varying stiffness of the rolling bearing and the transient response of the flexible rotor is considered. The Newmark-β integral method is used to solve the dynamic equation, and the relationship between the time-varying characteristics of bearing stiffness and load and the dynamic characteristics of the rotor is studied. The relationship between bearing stiffness and vibration strength is analyzed, and the influence of damage size on the time domain signal energy of the disc is analyzed. The results show that the model established in this paper can accurately reflect the dynamic interaction between the bearing and the rotor. With the extension of the bearing damage, the dynamic stiffness of the bearing attenuates, the intensity of the excitation force increases, and the vibration is transmitted to the disc, which affects the motion stability and vibration response of the disc. Full article

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17 pages, 3522 KiB

Open AccessArticle

A Formal Fuzzy Concept-Based Approach for Association Rule Discovery with Optimized Time and Storage

by Gamal F. Elhady, Haitham Elwahsh, Maazen Alsabaan, Mohamed I. Ibrahem and Ebtesam Shemis

Mathematics 2024, 12(22), 3590; https://doi.org/10.3390/math12223590 (registering DOI) - 16 Nov 2024

Abstract

Association Rule Mining (ARM) relies on concept lattices as an effective knowledge representation structure. However, classical ARM methods face significant limitations, including the generation of misleading rules during data-to-formal-context mapping and poor handling of heterogeneous data types such as linguistic, continuous, and imprecise [...] Read more.

Association Rule Mining (ARM) relies on concept lattices as an effective knowledge representation structure. However, classical ARM methods face significant limitations, including the generation of misleading rules during data-to-formal-context mapping and poor handling of heterogeneous data types such as linguistic, continuous, and imprecise data. This study aims to address these limitations by introducing a novel fuzzy data structure called the “fuzzy iceberg lattice” and its corresponding construction algorithm. The primary objectives of this study are to enhance the efficiency of extracting and visualizing frequent fuzzy closed item sets and to optimize both execution time and storage requirements. The necessity of this research stems from the high computational cost and redundancy associated with traditional fuzzy approaches, which, while capable of managing quantitative and imprecise data, are often impractical for large-scale applications in real scenarios. The proposed approach incorporates a ‘fuzzy min-max basis algorithm’ to derive exact and approximate rule bases from the extracted fuzzy closed item sets, eliminating redundancy while preserving valuable insights. Experimental results on benchmark datasets demonstrate that the proposed fuzzy iceberg lattice outperforms traditional fuzzy concept lattices, achieving an average reduction of 74.75% in execution time and 70.53% in memory usage. This efficiency gain, coupled with the lattice’s ability to handle crisp, quantitative, fuzzy, and heterogeneous data types, underscores its potential to advance ARM by yielding a manageable number of high-quality fuzzy concepts and rules. Full article

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15 pages, 1297 KiB

Open AccessArticle

Bus Schedule Time Prediction Based on LSTM-SVR Model

by Zhili Ge, Linbo Yang, Jiayao Li, Yuan Chen and Yingying Xu

Mathematics 2024, 12(22), 3589; https://doi.org/10.3390/math12223589 (registering DOI) - 16 Nov 2024

Abstract

With the acceleration of urbanization, urban bus scheduling systems are facing unprecedented challenges. Traditional bus scheduling provides the original schedule time and the planned time of arrival at the destination, where the schedule time is the departure time of the bus. However, various [...] Read more.

With the acceleration of urbanization, urban bus scheduling systems are facing unprecedented challenges. Traditional bus scheduling provides the original schedule time and the planned time of arrival at the destination, where the schedule time is the departure time of the bus. However, various factors encountered during the drive result in significant differences in the driving time of the bus. To ensure timely arrivals, the bus scheduling system has to rely on manual adjustments to optimize the schedule time to determine the actual departure time. In order to reduce the scheduling cost and align the schedule time closer to the actual departure time, this paper proposes a dynamic scheduling model, LSTM-SVR, which leverages the advantages of LSTM in capturing the time series features and the ability of SVR in dealing with nonlinear problems, especially its generalization ability in small datasets. Firstly, LSTM is used to efficiently capture features of multidimensional time series data and convert them into one-dimensional effective feature outputs. Secondly, SVR is used to train the nonlinear relationship between these one-dimensional features and the target variables. Thirdly, the one-dimensional time series features extracted from the test set are put into the generated nonlinear model for prediction to obtain the predicted schedule time. Finally, we validate the model using real data from an urban bus scheduling system. The experimental results show that the proposed hybrid LSTM-SVR model outperforms LSTM-BOA, SVR-BOA, and BiLSTM-SOA models in the accuracy of predicting bus schedule time, thus confirming the effectiveness and superior prediction performance of the model. Full article

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27 pages, 3723 KiB

Open AccessArticle

Industry 5.0 Drivers Analysis Using Grey-DEMATEL: A Logistics Case in Emerging Economies

by Chih-Hung Hsu, Shu-Jin Chen, Ming-Qiang Huang and Qi Le

Mathematics 2024, 12(22), 3588; https://doi.org/10.3390/math12223588 (registering DOI) - 16 Nov 2024

Abstract

The terms “Industry 5.0” and “smart logistics” have recently emerged as key concepts within the field of logistics. Nevertheless, the interconnection between these two concepts has been less extensively examined in academic literature, particularly in the context of emerging economies. In the contemporary [...] Read more.

The terms “Industry 5.0” and “smart logistics” have recently emerged as key concepts within the field of logistics. Nevertheless, the interconnection between these two concepts has been less extensively examined in academic literature, particularly in the context of emerging economies. In the contemporary business context, the logistics industry is seeking to advance sustainable development through the implementation of Industry 5.0. However, the industry is still in its nascent stages of realizing the transformation of smart logistics. Accordingly, the objective of this study is to identify the key drivers of Industry 5.0 in relation to the advancement of smart logistics in the logistics industry in emerging economies. In this study, the initial screening and identification of 15 core drivers was conducted using the fuzzy Delphi method. This involved the collation of the relevant literature and the collection of opinions from experts in the field. The identified drivers were then classified into three groups: sustainability, people-centricity, and resilience. Subsequently, the study adopted the Grey-DEMATEL method, which combines grey system theory with the decision making trial and evaluation laboratory (DEMATEL) technology. This approach enables the effective resolution of complex system issues characterized by uncertainty and incomplete information, facilitating the identification of causal relationships between the drivers and the construction of a centrality–causality outcome diagram. The study identified two key drivers: “government support policies” and “logistics standardization and infrastructure development”. This study represents a preliminary investigation into the ways managers, practitioners and policy makers can leverage Industry 5.0 to advance the field of smart logistics within the logistics industry. Full article

(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)

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11 pages, 861 KiB

Open AccessArticle

A Numerical Stability Analysis in the Inclusion of an Inverse Term in the Design of Experiments for Mixtures

by Javier Cruz-Salgado, Sergio Alonso-Romero, Edgar Augusto Ruelas-Santoyo, Israel Miguel-Andrés, Roxana Zaricell Bautista-López and Amir Hossein Nobil

Mathematics 2024, 12(22), 3587; https://doi.org/10.3390/math12223587 (registering DOI) - 16 Nov 2024

Abstract

A mixture experiment is one where the response depends only on the relative proportions of the ingredients present in the mixture. Different regression models are used to analyze mixture experiments, such as the Scheffé model, the Slack Variable model, and models with inverse [...] Read more.

A mixture experiment is one where the response depends only on the relative proportions of the ingredients present in the mixture. Different regression models are used to analyze mixture experiments, such as the Scheffé model, the Slack Variable model, and models with inverse terms. Models with inverse terms are worthy of consideration in certain applications. These models have been analyzed considering their fit quality, but not their numerical stability. This article analyzes the numerical stability of the model with inverse terms and the use of pseudo components. Likewise, a criterion is defined for the selection of the regression model with inverse terms, based on the quality of fit and numerical stability. Full article

(This article belongs to the Special Issue Advances in Mathematical Analytics and Operations Research)

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21 pages, 1043 KiB

Open AccessFeature PaperArticle

Large Sample Behavior of the Least Trimmed Squares Estimator

by Yijun Zuo

Mathematics 2024, 12(22), 3586; https://doi.org/10.3390/math12223586 (registering DOI) - 15 Nov 2024

Abstract

The least trimmed squares (LTS) estimator is popular in location, regression, machine learning, and AI literature. Despite the empirical version of least trimmed squares (LTS) being repeatedly studied in the literature, the population version of the LTS has never been introduced and studied. [...] Read more.

The least trimmed squares (LTS) estimator is popular in location, regression, machine learning, and AI literature. Despite the empirical version of least trimmed squares (LTS) being repeatedly studied in the literature, the population version of the LTS has never been introduced and studied. The lack of the population version hinders the study of the large sample properties of the LTS utilizing the empirical process theory. Novel properties of the objective function in both empirical and population settings of the LTS and other properties, are established for the first time in this article. The primary properties of the objective function facilitate the establishment of other original results, including the influence function and Fisher consistency. The strong consistency is established with the help of a generalized Glivenko–Cantelli Theorem over a class of functions for the first time. Differentiability and stochastic equicontinuity promote the establishment of asymptotic normality with a concise and novel approach. Full article

(This article belongs to the Special Issue Advances in High-Dimensional Data Analysis)

18 pages, 936 KiB

Open AccessArticle

Influence of Transfer Epidemiological Processes on the Formation of Endemic Equilibria in the Extended SEIS Model

by Alexander R. Karimov, Michael A. Solomatin and Alexey N. Bocharov

Mathematics 2024, 12(22), 3585; https://doi.org/10.3390/math12223585 (registering DOI) - 15 Nov 2024

Abstract

In the present paper, a modification of the standard mean-field model is considered, allowing for the description of the formation of a dynamic equilibrium between infected and recovered persons in a population of constant size. The key point of this model is that [...] Read more.

In the present paper, a modification of the standard mean-field model is considered, allowing for the description of the formation of a dynamic equilibrium between infected and recovered persons in a population of constant size. The key point of this model is that it highlights two-infection transfer mechanisms depending on the physical nature of the contact between people. We separate the transfer mechanism related directly to the movement of people (the so-called transport processes) from the one occurring at zero relative speed of persons (the so-called social contacts). Under the framework of a physical chemical analogy, the dependencies for the infection transfer rate constants are proposed for both purely transport and social mechanisms of spread. These dependencies are used in discussing the formation of quasi-stationary states in the model, which can be interpreted as endemic equilibrium states. The stability of such endemic equilibria is studied by the method of Lyapunov function. Full article

(This article belongs to the Special Issue Mathematical Methods and Models in Epidemiology)

13 pages, 880 KiB

Open AccessArticle

Image Processing Application for Pluripotent Stem Cell Colony Migration Quantification

by Timofey Chibyshev, Olga Krasnova, Alina Chabina, Vitaly V. Gursky, Irina Neganova and Konstantin Kozlov

Mathematics 2024, 12(22), 3584; https://doi.org/10.3390/math12223584 (registering DOI) - 15 Nov 2024

Abstract

Human pluripotent stem cells (hPSCs) attract tremendous attention due to their unique properties. Manual extraction of trajectories of cell colonies in experimental image time series is labor intensive and subjective, thus the aim of the work was to develop a computer semi-automated protocol [...] Read more.

Human pluripotent stem cells (hPSCs) attract tremendous attention due to their unique properties. Manual extraction of trajectories of cell colonies in experimental image time series is labor intensive and subjective, thus the aim of the work was to develop a computer semi-automated protocol for colony tracking. The developed procedure consists of three major stages, namely, image registration, object detection and tracking. Registration using discrete Fourier transform and tracking based on the solution of a linear assignment problem was implemented as console programs in the Python 3 programming language using a variety of packages. Object detection was implemented as a multistep procedure in the ProStack in-house software package. The procedure consists of more than 40 elementary operations that include setting of several biologically relevant parameters, image segmentation and performing of quantitative measurements. The developed procedure was applied to the dataset containing bright-field images from time-lapse recording of the human embryonic cell line H9. The detection step took about 6 hours for one image time series with a resolution of 2560 by 2160; about 1 min was required for image registration and trajectories extraction. The developed procedure was effective in detecting and analyzing the time series of images with “good” and “bad” phenotypes. The differences between phenotypes in the distance in pixels between the starting and finishing positions of trajectories, in the path length along the trajectory, and the mean instant speed and mean instant angle of the trajectories were identified as statistically significant by Mann–Whitney and Student’s tests. The measured area and perimeter of the detected colonies differed, on average, for different phenotypes throughout the entire time period under consideration. This result confirms previous findings obtained by analyzing static images. Full article

(This article belongs to the Special Issue Image Processing and Machine Learning with Applications)

19 pages, 8125 KiB

Open AccessArticle

A Hybrid Deep Learning Framework for OFDM with Index Modulation Under Uncertain Channel Conditions

by Md Abdul Aziz, Md Habibur Rahman, Rana Tabassum, Mohammad Abrar Shakil Sejan, Myung-Sun Baek and Hyoung-Kyu Song

Mathematics 2024, 12(22), 3583; https://doi.org/10.3390/math12223583 (registering DOI) - 15 Nov 2024

Abstract

Index modulation (IM) is considered a promising approach for fifth-generation wireless systems due to its spectral efficiency and reduced complexity compared to conventional modulation techniques. However, IM faces difficulties in environments with unpredictable channel conditions, particularly in accurately detecting index values and dynamically [...] Read more.

Index modulation (IM) is considered a promising approach for fifth-generation wireless systems due to its spectral efficiency and reduced complexity compared to conventional modulation techniques. However, IM faces difficulties in environments with unpredictable channel conditions, particularly in accurately detecting index values and dynamically adjusting index assignments. Deep learning (DL) offers a potential solution by improving detection performance and resilience through the learning of intricate patterns in varying channel conditions. In this paper, we introduce a robust detection method based on a hybrid DL (HDL) model designed specifically for orthogonal frequency-division multiplexing with IM (OFDM-IM) in challenging channel environments. Our proposed HDL detector leverages a one-dimensional convolutional neural network (1D-CNN) for feature extraction, followed by a bidirectional long short-term memory (Bi-LSTM) network to capture temporal dependencies. Before feeding data into the network, the channel matrix and received signals are preprocessed using domain-specific knowledge. We evaluate the bit error rate (BER) performance of the proposed model using different optimizers and equalizers, then compare it with other models. Moreover, we evaluate the throughput and spectral efficiency across varying SNR levels. Simulation results demonstrate that the proposed hybrid detector surpasses traditional and other DL-based detectors in terms of performance, underscoring its effectiveness for OFDM-IM under uncertain channel conditions. Full article

(This article belongs to the Special Issue Advanced Algorithms in Wireless Communication and Internet of Things (IoT))

25 pages, 2169 KiB

Open AccessReview

Review of the Natural Time Analysis Method and Its Applications

by Panayiotis A. Varotsos, Efthimios S. Skordas, Nicholas V. Sarlis and Stavros-Richard G. Christopoulos

Mathematics 2024, 12(22), 3582; https://doi.org/10.3390/math12223582 (registering DOI) - 15 Nov 2024

Abstract

A new concept of time, termed natural time, was introduced in 2001. This new concept reveals unique dynamic features hidden behind time-series originating from complex systems. In particular, it was shown that the analysis of natural time enables the study of the dynamical [...] Read more.

A new concept of time, termed natural time, was introduced in 2001. This new concept reveals unique dynamic features hidden behind time-series originating from complex systems. In particular, it was shown that the analysis of natural time enables the study of the dynamical evolution of a complex system and identifies when the system enters a critical stage. Hence, natural time plays a key role in predicting impending catastrophic events in general. Several such examples were published in a monograph in 2011, while more recent applications were compiled in the chapters of a new monograph that appeared in 2023. Here, we summarize the application of natural time analysis in various complex systems, and we review the most recent findings of natural time analysis that were not included in the previously published monographs. Specifically, we present examples of data analysis in this new time domain across diverse fields, including condensed-matter physics, geophysics, earthquakes, volcanology, atmospheric sciences, cardiology, engineering, and economics. Full article

(This article belongs to the Special Issue Recent Advances in Time Series Analysis)

19 pages, 1003 KiB

Open AccessArticle

Inverse Coefficient Problem for Epidemiological Mean-Field Formulation

by Viktoriya Petrakova

Mathematics 2024, 12(22), 3581; https://doi.org/10.3390/math12223581 (registering DOI) - 15 Nov 2024

Abstract

The paper proposes an approach to solving the inverse epidemiological problem, written in terms of the “mean-field” theory. Finding the coefficients of an epidemiological SIR mean-field model is reduced to solving an optimization problem, for the solution of which only zero-order methods can [...] Read more.

The paper proposes an approach to solving the inverse epidemiological problem, written in terms of the “mean-field” theory. Finding the coefficients of an epidemiological SIR mean-field model is reduced to solving an optimization problem, for the solution of which only zero-order methods can be used. An algorithm for the solution of the inverse coefficient problem is proposed. Computational experiments were carried out to compare the obtained solutions with respect to synthetic and real data. The results of computational experiments have shown the efficiency of this approach. Ways to further improve the approach have also been determined. Full article

(This article belongs to the Special Issue Applied Mathematics in Disease Control and Dynamics)

26 pages, 1159 KiB

Open AccessArticle

FEBE-Net: Feature Exploration Attention and Boundary Enhancement Refinement Transformer Network for Bladder Tumor Segmentation

by Chao Nie, Chao Xu and Zhengping Li

Mathematics 2024, 12(22), 3580; https://doi.org/10.3390/math12223580 (registering DOI) - 15 Nov 2024

Abstract

The automatic and accurate segmentation of bladder tumors is a key step in assisting urologists in diagnosis and analysis. At present, existing Transformer-based methods have limited ability to restore local detail features and insufficient boundary segmentation capabilities. We propose FEBE-Net, which aims to [...] Read more.

The automatic and accurate segmentation of bladder tumors is a key step in assisting urologists in diagnosis and analysis. At present, existing Transformer-based methods have limited ability to restore local detail features and insufficient boundary segmentation capabilities. We propose FEBE-Net, which aims to effectively capture global and remote semantic features, preserve more local detail information, and provide clearer and more precise boundaries. Specifically, first, we use PVT v2 backbone to learn multi-scale global feature representations to adapt to changes in bladder tumor size and shape. Secondly, we propose a new feature exploration attention module (FEA) to fully explore the potential local detail information in the shallow features extracted by the PVT v2 backbone, eliminate noise, and supplement the missing fine-grained details for subsequent decoding stages. At the same time, we propose a new boundary enhancement and refinement module (BER), which generates high-quality boundary clues through boundary detection operators to help the decoder more effectively preserve the boundary features of bladder tumors and refine and adjust the final predicted feature map. Then, we propose a new efficient self-attention calibration decoder module (ESCD), which, with the help of boundary clues provided by the BER module, gradually and effectively recovers global contextual information and local detail information from high-level features after calibration enhancement and low-level features after exploration attention. Extensive experiments on the cystoscopy dataset BtAMU and five colonoscopy datasets have shown that FEBE-Net outperforms 11 state-of-the-art (SOTA) networks in segmentation performance, with higher accuracy, stronger robust stability, and generalization ability. Full article

(This article belongs to the Special Issue Medical Imaging Analysis with Artificial Intelligence)

28 pages, 394 KiB

Open AccessArticle

Error Analysis for Semilinear Stochastic Subdiffusion with Integrated Fractional Gaussian Noise

by Xiaolei Wu and Yubin Yan

Mathematics 2024, 12(22), 3579; https://doi.org/10.3390/math12223579 (registering DOI) - 15 Nov 2024

Abstract

We analyze the error estimates of a fully discrete scheme for solving a semilinear stochastic subdiffusion problem driven by integrated fractional Gaussian noise with a Hurst parameter

H \in (0, 1)

. The covariance operator Q of the stochastic fractional [...] Read more.

We analyze the error estimates of a fully discrete scheme for solving a semilinear stochastic subdiffusion problem driven by integrated fractional Gaussian noise with a Hurst parameter

H \in (0, 1)

. The covariance operator Q of the stochastic fractional Wiener process satisfies

∥ A^{- ρ} Q^{1 / 2} ∥_{H S} < \infty

for some

ρ \in [0, 1)

, where

{∥ \cdot ∥}_{H S}

denotes the Hilbert–Schmidt norm. The Caputo fractional derivative and Riemann–Liouville fractional integral are approximated using Lubich’s convolution quadrature formulas, while the noise is discretized via the Euler method. For the spatial derivative, we use the spectral Galerkin method. The approximate solution of the fully discrete scheme is represented as a convolution between a piecewise constant function and the inverse Laplace transform of a resolvent-related function. By using this convolution-based representation and applying the Burkholder–Davis–Gundy inequality for fractional Gaussian noise, we derive the optimal convergence rates for the proposed fully discrete scheme. Numerical experiments confirm that the computed results are consistent with the theoretical findings. Full article

(This article belongs to the Section Computational and Applied Mathematics)

23 pages, 437 KiB

Open AccessArticle

On a Class of Nonlinear Waves in Microtubules

by Nikolay K. Vitanov, Alexandr Bugay and Nikolay Ustinov

Mathematics 2024, 12(22), 3578; https://doi.org/10.3390/math12223578 (registering DOI) - 15 Nov 2024

Abstract

Microtubules are the basic components of the eukaryotic cytoskeleton. We discuss a class of nonlinear waves traveling in microtubules. The waves are obtained on the basis of a kind of z-model. The model used is extended to account for (i) the possibility [...] Read more.

Microtubules are the basic components of the eukaryotic cytoskeleton. We discuss a class of nonlinear waves traveling in microtubules. The waves are obtained on the basis of a kind of z-model. The model used is extended to account for (i) the possibility for nonlinear interaction between neighboring dimers and (ii) the possibility of asymmetry in the double-well potential connected to the external electric field caused by the interaction of a dimer with all the other dimers. The model equation obtained is solved by means of the specific case of the Simple Equations Method. This specific case is denoted by SEsM(1,1), and the equation of Riccati is used as a simple equation. We obtain three kinds of waves with respect to the relation of their velocity with the specific wave velocity

v_{c}

determined by the parameters of the dimer: (i) waves with

v > v_{c}

, which occur when there is nonlinearity in the interaction between neighboring dimers; (ii) waves with

v < v_{c}

(they occur when the interaction between neighboring dimers is described by Hooke’s law); and (iii) waves with

v = v_{c}

. We devote special attention to the last kind of waves. In addition, we discuss several waves which travel in the case of the absence of friction in a microtubule system. Full article

16 pages, 3431 KiB

Open AccessArticle

Sample Inflation Interpolation for Consistency Regularization in Remote Sensing Change Detection

by Zuo Jiang, Haobo Chen and Yi Tang

Mathematics 2024, 12(22), 3577; https://doi.org/10.3390/math12223577 (registering DOI) - 15 Nov 2024

Abstract

Semi-supervised learning has gained significant attention in the field of remote sensing due to its ability to effectively leverage both a limited number of labeled samples and a large quantity of unlabeled data. An effective semi-supervised learning approach utilizes unlabeled samples to enforce [...] Read more.

Semi-supervised learning has gained significant attention in the field of remote sensing due to its ability to effectively leverage both a limited number of labeled samples and a large quantity of unlabeled data. An effective semi-supervised learning approach utilizes unlabeled samples to enforce prediction consistency under minor perturbations, thus reducing the model’s sensitivity to noise and suppressing false positives in change-detection tasks. This principle underlies consistency regularization-based methods. However, while these methods enhance noise robustness, they also risk overlooking subtle but meaningful changes, leading to information loss and missed detections. To address this issue, we introduce a simple yet efficient method called Sample Inflation Interpolation (SII). This method leverages labeled sample pairs to mitigate the information loss caused by consistency regularization. Specifically, we propose a novel data augmentation strategy that generates additional change samples by combining existing supervised change samples with calculated proportions of change areas. This approach increases both the quantity and diversity of change samples in the training set, effectively compensating for potential information loss and reducing missed detections. Furthermore, to prevent overfitting, small perturbations are applied to the generated sample pairs and their labels. Experiments conducted on two public change detection (CD) datasets validate the effectiveness of our proposed method. Remarkably, even with only 5% of labeled training data, our method achieves performance levels that closely approach those of fully supervised learning models. Full article

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19 pages, 17340 KiB

Open AccessArticle

TTG-Text: A Graph-Based Text Representation Framework Enhanced by Typical Testors for Improved Classification

by Carlos Sánchez-Antonio, José E. Valdez-Rodríguez and Hiram Calvo

Mathematics 2024, 12(22), 3576; https://doi.org/10.3390/math12223576 (registering DOI) - 15 Nov 2024

Abstract

Recent advancements in graph-based text representation, particularly with embedding models and transformers such as BERT, have shown significant potential for enhancing natural language processing (NLP) tasks. However, challenges related to data sparsity and limited interpretability remain, especially when working with small or imbalanced [...] Read more.

Recent advancements in graph-based text representation, particularly with embedding models and transformers such as BERT, have shown significant potential for enhancing natural language processing (NLP) tasks. However, challenges related to data sparsity and limited interpretability remain, especially when working with small or imbalanced datasets. This paper introduces TTG-Text, a novel framework that strengthens graph-based text representation by integrating typical testors—a symbolic feature selection technique that refines feature importance while reducing dimensionality. Unlike traditional TF-IDF weighting, TTG-Text leverages typical testors to enhance feature relevance within text graphs, resulting in improved model interpretability and performance, particularly for smaller datasets. Our evaluation on a text classification task using a graph convolutional network (GCN) demonstrates that TTG-Text achieves a 95% accuracy rate, surpassing conventional methods and BERT with fewer required training epochs. By combining symbolic algorithms with graph-based models, this hybrid approach offers a more interpretable, efficient, and high-performing solution for complex NLP tasks. Full article

(This article belongs to the Special Issue Recent Trends and Advances in the Natural Language Processing)

21 pages, 495 KiB

Open AccessArticle

On the Evolution Operators of a Class of Linear Time-Delay Systems

by Manuel De la Sen

Mathematics 2024, 12(22), 3575; https://doi.org/10.3390/math12223575 (registering DOI) - 15 Nov 2024

Abstract

This paper studies the properties of the evolution operators of a class of time-delay systems with linear delayed dynamics [...] Full article

(This article belongs to the Special Issue New Trends in Nonlinear Analysis)

31 pages, 474 KiB

Open AccessArticle

Analysis of a Mathematical Model of Zoonotic Visceral Leishmaniasis (ZVL) Disease

by Goni Umar Modu, Suphawat Asawasamrit, Abdulfatai Atte Momoh, Mathew Remilekun Odekunle, Ahmed Idris and Jessada Tariboon

Mathematics 2024, 12(22), 3574; https://doi.org/10.3390/math12223574 (registering DOI) - 15 Nov 2024

Abstract

This research paper attempts to describe the transmission dynamic of zoonotic visceral leishmaniasis with the aid of a mathematical model by considering the asymptomatic stages in humans and animals. The disease is endemic in several countries. Data used in the research are obtained [...] Read more.

This research paper attempts to describe the transmission dynamic of zoonotic visceral leishmaniasis with the aid of a mathematical model by considering the asymptomatic stages in humans and animals. The disease is endemic in several countries. Data used in the research are obtained from the literature while some are assumed based on the disease dynamic. The consideration of both asymptomatic and the symptomatic infected individuals is incorporated in both humans and animals (reservoir), as well as lines of treatment for the human population. It is found that the model has two fixed points; the VL-free fixed point and the VL-endemic fixed point. Stability analysis of the fixed points shows that the VL-free fixed point is globally asymptotically stable whenever the basic reproduction number is less than one and the VL-endemic fixed point is globally asymptotically stable whenever the basic reproduction number is greater than one. Sensitivity analysis is conducted for the parameters in the basic reproduction number, and the profile of each state variable is also depicted using the data obtained from the literature and those assumed. The transmission probability from infected sandflies to animals, transmission probability from infected animals to sandflies, per capita biting rate of sandflies of animals, and rate of transfer from symptomatic infected animals to the recovered class are among the most sensitive parameters that have the greatest influence on the basic reproduction number. Moreover, the value of the basic reproduction number is obtained to be 0.98951, which may require further study, as the margin between potential disease control and outbreak is thin. Full article

(This article belongs to the Special Issue Mathematical Biology and Its Applications to Disease Modeling)

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